Title :
L-Networks: A Topological Model for Regular 2D Interconnection Networks
Author :
Camarero, Cristobal ; Martinez, Carlos ; Beivide, Ramon
Author_Institution :
Dept. de Electron. y Comput., Univ. de Cantabria, Santander, Spain
Abstract :
A complete family of Cayley graphs of degree four, denoted as L-networks, is considered in this paper. L-networks are 2D mesh-based topologies with wrap-around connections. L-networks constitute a graph-based model which englobe many previously proposed 2D interconnection networks. Some of them have been extensively used in the industry as the underlying topology for parallel and distributed computers of different scales. Tori, twisted and doubly twisted tori, toroidal diagonal meshes, chordal rings, and circulant graphs are, among others, members of the L-network family. Therefore, many results obtained in previous studies on these networks can be deduced from the general framework presented in this work. In addition, the network model presented in this work allows for new results on the domain of low-degree interconnection networks. Particularly, closed expressions for the graph distance properties have been derived and an optimal routing algorithm of constant complexity is provided. Since symmetry has a big impact on network performance, we have also identified which L-networks are symmetric by studying their group of automorphisms. Finally, a very simple model that predicts the performance of L-networks is also presented. Such model has been contrasted with empirical evaluation.
Keywords :
multiprocessor interconnection networks; telecommunication network topology; 2D mesh-based topologies; Cayley graphs; L-networks; chordal rings; circulant graphs; distributed computers; doubly twisted tori; graph-based model; low-degree interconnection networks; network model; parallel computers; regular 2D interconnection networks; topological model; toroidal diagonal meshes; wrap-around connections; Computational modeling; Computers; Layout; Multiprocessor interconnection; Network topology; Topology; Vectors; Computational modeling; Computers; Layout; Multiprocessor interconnection; Network topology; Topologies; Topology; Vectors; circulant graphs; graphs; interconnection networks; performance; ring; tori;
Journal_Title :
Computers, IEEE Transactions on